Approximation of Elliptic Boundary-Value Problems

Approximation of Elliptic Boundary-Value Problems
Author :
Publisher : Courier Corporation
Total Pages : 386
Release :
ISBN-10 : 9780486457918
ISBN-13 : 0486457915
Rating : 4/5 (915 Downloads)

Book Synopsis Approximation of Elliptic Boundary-Value Problems by : Jean-Pierre Aubin

Download or read book Approximation of Elliptic Boundary-Value Problems written by Jean-Pierre Aubin and published by Courier Corporation. This book was released on 2007-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis and to explain its applications to approximation of nonhomogeneous boundary-value problems for elliptic operators. The treatment begins with a summary of the main results established in the book. Chapter 1 introduces the variational method and the finite-difference method in the simple case of second-order differential equations. Chapters 2 and 3 concern abstract approximations of Hilbert spaces and linear operators, and Chapters 4 and 5 study finite-element approximations of Sobolev spaces. The remaining four chapters consider several methods for approximating nonhomogeneous boundary-value problems for elliptic operators.


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